function T = transferEntropyRank(X,Y,l,k,t,w,Q)
% This function computes the transfer entropy between time series X and Y,
% with the flow of information directed from X to Y, after ranking both X and Y. Probability density
% estimation is based on bin counting with fixed and equally-spaced bins.
% For details, please see T Schreiber, "Measuring information transfer", Physical Review Letters, 85(2):461-464, 2000.
% X: first time series in 1-D vector
% Y: second time series in 1-D vector
% l: block length for X
% k: block length for Y
% t: time lag in X from present to where the block of length l ends
% w: time lag in Y from present to where the block of length k ends
% Q: number of quantization levels for both X and Y
% T: transfer entropy (bits)
% Copyright 2011 Joon Lee
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% ordinal sampling (ranking)
% quantize X and Y according to fixed, equally-spaced bins
% go through the time series X and Y, and populate Xpat, Ypat, and Yt
Xpat=; Ypat=; Yt=;
for i=max([l+t k+w]):1:min([length(Xq) length(Yq)])
% compute transfer entropy
p1=sum(Xpat==Xpat(i) & Ypat==Ypat(i) & Yt==Yt(i))/N;
p2=sum(Xpat==Xpat(i) & Ypat==Ypat(i) & Yt==Yt(i))/sum(Xpat==Xpat(i) & Ypat==Ypat(i));
p3=sum(Ypat==Ypat(i) & Yt==Yt(i))/sum(Ypat==Ypat(i));
idxDone=[idxDone; find(Xpat==Xpat(i) & Ypat==Ypat(i) & Yt==Yt(i))];